Binary Bose-Chaudhuri-Hocquenghem (BCH) codes are commonly used error correcting codes in modern communication systems. Long BCH codes with block lengths of 32400 bits or longer are used as the outer forward error correcting code in the second generation Digital Video Broadcasting (DVB-S2) Standard from the European Telecommunications Standard Institute (ESTI). Recently, long BCH codes have been investigated for the on-chip error correction of multilevel NAND flash memories. Binary BCH codes are also used in disk drive systems. In many of these applications of BCH codes, the BCH coder-decoder is implemented in hardware, such as an application specific integrated circuit (ASIC). It would be desirable if BCH codes could be implemented in a manner that reduces power consumption and/or size. Systems that include such a BCH component could be made smaller, could operate longer off of a battery, etc.